Dicier than Dice
Frank Knight in his dissertation Risk, Uncertainty and Profit (1921) made a distinction between risk and uncertainty.
With risk he states you have the ability to project future outcomes on the basis of a probability distribution. In other words, you can estimate the likelihood of a particular event within a reasonably precise confidence interval. This is similar, some of us may remember, to the concept of expected value where you quantify the potential payout or loss of a specific choice by multiplying the payout/loss amount times the probability that it will occur.
Before you roll a pair of dice you can compute the likelihood of rolling any number between 2 and 12. If there are payouts or costs associated with rolling particular numbers you can compute exactly what you might risk or gain before you enter into a particular dice game.
This type of analysis is used to develop a business case. A valid business case is one in which the expected reward is well understood, as well as the probability of success or failure. If the expected reward is a million dollars and the cost of development (the bet) is $200,000 and the likelihood of success is 80 percent, the expected value is $640,000 (1,000,000 – 200,000* .8). This means that if you did this project many times the multiple you would expect to make on your investment would converge on 320%. However, if you did it once you would have a 4 out of 5 chance of an $800,000 return and a 1 out of 5 chance of losing 200,000. If losing $200,000 would put you out of business this may be considered too risky. If you had a lot of money, you could do the project multiple times. This would allow you to reduce your overall risk of losing money but at the expense of expecting a lower average return.
High risk/high return is as rational as low risk/low return. If it cost you $10k to drill for oil and the chance of finding it is 1% but if you find it you make 10 million dollars, it makes sense to drill for oil. However, if you only have $100,000 you may find it too risky to try. However, if you have $10 million it’s a no brainer to try. Even though the market value of a successful outcome is the same for everybody, the value of available capital is relative to the specific circumstances of the investor. This example demonstrates that when you have a large amount of capital you actually have a better chance of securing a positive return over the long term because you can distribute risk over time in a way that with a small amount of capital you cannot. We might call this the rich get richer rule.
So if you have enough money in your pocket and the payout is high enough it could be a “no brainer” to enter a dice game even if you needed snake eyes to win. However, what if you had to make a bet but you did not know what the payout would be? Or what if you knew what the payout would be but you had no way of estimating the chance of rolling your point? We now enter the realm of uncertainty.
Knight defined uncertainty as the state in which you cannot estimate the probability of an anticipated outcome.
Humans are very adverse to Knightian uncertainty. Right before the original gulf war, the stock market tanked. When war was declared the market went up. If war had not been declared it would have gone up as well. It was the uncertainty of not knowing that induced the broadly felt pessimism. It’s well established that humans are irrationally biased against negative outcomes (Let me know if you would like a reference). As a kind of corollary, if an outcome is a Knightian uncertainty, people will tend to assume things will turn out bad rather than the reverse. In fact, people treat uncertainty as dicier than dice.
June 2nd, 2009 at 11:52 am
[...] This post was Twitted by csterwa – Real-url.org [...]